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This topic solves trigonometric equations such as sin x = 0.5 over a given interval, finding all solutions using the CAST diagram or graph symmetry, including equations needing rearranging or an identity. It appears across A-Level and iAL Pure Maths with the major exam boards. Work through it free on eClassroom, with clear worked examples and instantly-marked questions that build your confidence for the exam.
How you do it
Find the principal value with the inverse function, then use the symmetry of the graph to get every solution in the range. Sketch the curve and draw the horizontal line across it — the number of intersections tells you how many answers to find. Widen the interval first if the angle is doubled.
Before you start
The groundwork here is trig graphs and exact values. It belongs to the Pure 2 specification. It carries straight through to identities and harder equations. The topic sits within Trigonometry.
What you learn
Finding every solution in a given range is the core P2 skill. First, find the base angle from the calculator using the positive value. Many equations become a quadratic in one trig function. The course works through solving in a given range, rearranging into a quadratic, transformed argument: the range shifts, transformed argument: the range scales, two-step arguments: scale and shift and ‘Show that’, then solve. Every section has instant-feedback practice questions matched to Edexcel International A-Level and 9MA0 Pure, and the course finishes with full exam-style questions you mark yourself.
Related Topics
Solving Trig Equations is a Trigonometry topic in the A-level syllabus, covered here at the AS year. The course is built from 6 concept sections, 6 worked examples and 6 check points before the exam-style set. Related topics students usually take next include Trig Graphs & Transformations, Trig Identities (C12), Trig Ratios & Exact Values, Addition Formulae and Double Angle Formulae. For unlimited practice, the Trigonometry revision engine builds new questions on demand and records your accuracy.
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